“This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study

Lifeas Kudakwashe Kapofu; Winfilda Kapofu

doi:10.29333/iejme/8446

Full Text (PDF)

Lifeas Kudakwashe Kapofu ¹ ^* , Winfilda Kapofu ²

More Detail

¹ Department of Education Australia, AUSTRALIA² Durban Girls' Secondary School, SOUTH AFRICA^* Corresponding Author

Abstract

Integration of history of mathematics (HOM) in mathematics education is emerging as frontier endowed with utility to stem decline in uptake, enhance performance and alter the negative perceptions about the subject. This case study sought to explore the influence of history of mathematics on grade eleven girls’ perceptions of the Theorem of Pythagoras in particular and mathematics in general. In this exploratory study, the genetic approach of HOM was used in teaching the Theorem of Pythagoras. Findings indicate that the inclusion of aspects of the history of mathematics catalysed positive learner perceptions of the Theorem and mathematics in general. Notable changes in learner perceptions included affirmations of an increased level of motivation and confessed improvement in readiness of grade eleven learners in tackling challenging tasks involving the Theorem of Pythagoras. Learners also alluded to increased confidence in dealing with proofs, enjoying making their own discoveries and solving mathematical problems in general.

Keywords

history of mathematics
Pythagoras Theorem
integration
learner perceptions
influence of history of mathematics

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2020, Volume 15, Issue 3, Article No: em0604

https://doi.org/10.29333/iejme/8446

Publication date: 31 Jul 2020

Article Views: 2434

Article Downloads: 1412

Open Access References How to cite this article

References

Anderson, R. (2007). Being a mathematics learner: Four faces of identity. Mathematics Educator, 17(1), 1 - 14.
Babbie, E. (1990). Survey research methods (2nd ed.): Belmont, California: Wadsworth Publishing Company.
Barbin, E. (2000). Integrating history: Research perspectives. In J. Fauvel & J. van Maanen (Ed.), History in mathematics education: An ICMI book (pp. 63 - 90). Dordrecht, Netherlands: Kluwer Academic Publishers.
Barry, D. T. (2014). Mathematics in search history. Mathematics Teacher, 93(8), 647-650.
Bidwell, J. K. (1993). Humanize your classroom with the history of mathematics. The Mathematics Teacher, 461-464.
Bogdan, R. C., & Biklen, S. K. (1992). Qualitative research for education: An introduction to theory and methods. Needham Heights, MA: Allyn & Bacon.
Bütüner, S. Ö., & Baki, A. (2020). The Use of History of Mathematics in the Mathematics Classroom: An Action Study. International Journal of Education in Mathematics, Science and Technology, 8(2), 92-117. https://doi.org/10.46328/ijemst.v8i2.843
Carter, P., Dunne, L., Morgan, H., & Smuts, C. (2006). Mathematics: Grade 9 Learners’ book NCS. Cape Town, South Africa: Cambridge University Press.
Clark, K. (2019, February). History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future. In Eleventh Congress of the European Society for Research in Mathematics Education. Freudenthal Group; Freudenthal Institute; ERME.
Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (2018). Mathematics, Education and History. Towards a harmonious partnership. ICME-13 monographs. Cham: Springer. https://doi.org/10.1007/978-3-319-73924-3
Cohen, L., Manion, L., & Morrison, K. (2013). Research methods in education. London, Routledge, Taylor & Francis Group. https://doi.org/10.4324/9780203720967
Collingwood, R. G., & Collingwood, R. G. (1994). The idea of history. Oxford University Press on Demand.
De Villiers, M. (2008). Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining. Pythagoras, Journal of AMESA, 32-40. https://doi.org/10.4102/pythagoras.v0i68.65
Denzin, N. K., & Lincoln, Y. S. (2005). Handbook of qualitative research (3rd ed.): London, Sage Publications.
Department of Basic Education. (2010). National Curriculum Statement. Pretoria: Government Print.
Department of Basic Education. (2011). “Curriculum and Assessment Policy Statement” (CAPS).
Department of Education. (2002). Revised National Curriculum Statement (Grade R - 9). Pretoria.
Department of Education. (2014). Matric Results Analysis Report (Grade 12). Pretoria.
Department of Education. (May 2002). Revised National Curriculum Statement (RNCS) Grades R-9 (Schools): Mathematics (Vol. Gazette No.: 23406, Vol. 443). Pretoria.
Dinaledi Zenex Foundation. (2007). Putting Language into the mathematics and science equation. South Africa: Dinaledi.
Entwistle, N., & Smith, C. (2002). Personal understanding and target understanding: Mapping influences on the outcomes of learning. British Journal of Educational Psychology, 72(3), 321-342. https://doi.org/10.1348/000709902320634528
Eves, H. W. (1976). An introduction to the history of mathematics.
Felder, R. M., & Brent, R. (2007). Cooperative learning, Education designs. In P. A. Mabrouk (Ed.), Active learning: Models from analytical sciences (pp. 35 - 53). Washington DC: American Chemical society. https://doi.org/10.1021/bk-2007-0970.ch004
Fox, N., Hunn, A., & Mathers, N. (2002). Sampling, Trent Focus Group.
Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Springer Science & Business Media.
Fried, M. N., Guillemette, D., & Jahnke, H. N. (2016, July). Theoretical and/or conceptual frameworks for integrating history in mathematics education.
Furinghetti, F. (2000). The history of mathematics as a coupling link between secondary and university teaching: International Journal of Mathematics Education in Science and Technology, 31(1), 43-51. https://doi.org/10.1080/002073900287372
Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131-143. https://doi.org/10.1007/s10649-006-9070-0
Furinghetti, F., & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: from philogenesis and ontogenesis theory to classroom practice. In Handbook of international research in mathematics education (pp. 643-666). Routledge.
Goktepe, S., & Ozdemir, A. S. (2013). An example of using history of mathematics in classes. European Journal of Science and Mathematics Education, 1(3), 125-136.
González, G., & Herbst, P. G. (2006). Competing arguments for the geometry course: Why were American high school students supposed to study geometry in the twentieth century? International Journal for the History of Mathematics Education, 1(1), 7-33.
Hanna, G. (1998). Proof as explanation in geometry. Focus on learning problems in mathematics, 20, 4-13.
Hartley, M. S., & Treagust, D. F. (2014). Learner perceptions of the introduction of computer-assisted learning in mathematics at a peri-urban school in South Africa. Learning Environments Research, 17(1), 95-111. https://doi.org/10.1007/s10984-014-9157-y
Horton, L. B., & Panasuk, R. M. (2013). Integrating History of Mathematics into the Classroom: Was Aristotle wrong?, 1927-2677. Retrieved from www.sciedu.ca/jct website.
Hoyrup, J. (1994). In measure, number, and weight, Studies in mathematics and culture. SUNY Press.
Jankvist, U. T. (2009). History of modern applied mathematics in mathematics education. For the learning of mathematics, 29(1), 8-13.
Kaplan, B., & Maxwell, J. A. (1994). Qualitative research methods for evaluating computer information systems. In J. G. Anderson, C. E. Anderson, & S. J. Jay, (Eds.), Evaluating health care information systems: Method and application. California: Sage Publications.
Karp, A. (2014). The history of mathematics education: Developing a research methodology. In Handbook on the history of mathematics education (pp. 9-24). Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9155-2_2
Kilpatrick, J. (2020). History of research in mathematics education. Encyclopedia of mathematics education, 349-354. https://doi.org/10.1007/978-3-030-15789-0_71
Kraak, A. (2015). The National Skills Development Strategy: a new institutional regime for skills formation in post-apartheid South Africa.
Laridon, P. (2006). Classroom Mathematics: Grade 8 Learners’ book. Sandton, SA Heinemann Publishers (Pty) Ltd.
Moretti, V., & Radford, L. (2016, July). Towards a culturally meaningful history of concepts and the organization of mathematics teaching activity. In Radford, L., Furinghetti, F., & Hausberger, T. (Eds.), Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics (pp. 503-512). Montpellier, France: IREM de Montpellier.
Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), 1-11. https://doi.org/10.15700/saje.v40n1a1727
Pehkonen, E., & Torner, G. (1998). The state of the art in mathematics- related belief research: Results of the MAVI activities. Helsinki, Finland: University of Helsinki.
Polya, G. (1963). Studies in Mathematics. Stanford. School Mathematics Groups.
Radebe, K. (2013). Beyond Matric Results, the deeper picture. Johannesburg, Gauteng, South Africa. Retrieved from http://www.moneyweb.co.za/moneyweb-SouthAfrica
Radford, L. (2015). Of love, frustrations and mathematics: A cultural-historical approach to emotions in mathematics teaching and learning. In B. Pepin, & B. Roesken-Winter (Eds.). From beliefs to dynamic affect systems in mathematics education: Advances in mathematics education (pp. 25 - 49). Manchester: Springer International Publishing.
Radford, L., Furinghetti, F., & Katz, V. (2007). Introduction The topos of meaning or the encounter between past and present. Educational Studies in Mathematics, 66(2), 107-110. https://doi.org/10.1007/s10649-006-9076-7
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334 - 370). New York: Macmillan.
Schwandt, T. A. (2002). Three epistemological stances for qualitative inquiry. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (3rd ed.): London, Sage Publications.
Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM, 47(3), 319-329. https://doi.org/10.1007/s11858-015-0693-4
Siu, M. K. (2004). History and pedagogy of mathematics: No, I do not use history of mathematics in my class. Why? Paper presented at the Proceedings of HPM Upsalla.
Siu, M. K., & Tzanakis, C. (2004). History of mathematics in classroom teaching-appetizer? Main course? Or dessert. Mediterranean Journal for Research in Mathematics Education, 3(1-2), v-x.
Torerai, E. (2013, 06 Dec.). Results disappointed us, The New Age. Retrieved from http://www.thenewage.co.za/mobi/Detail.aspx?NewsID=73094&Cat=1017
Van de Walle, J. A. (2004). Elementary and Middle School Mathematics: Teaching developmentally. Boston: Pearson.
Wong, K. Y. (2004). Add Cultural Values to Mathematics Instruction. Singapore: National Institute of Education.
Yin, R. (2017). Case Study Research: Design and Method. Newbury Park, CA: Sage Publications.

How to cite this article

APA

Kapofu, L. K., & Kapofu, W. (2020). “This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study. International Electronic Journal of Mathematics Education, 15(3), em0604. https://doi.org/10.29333/iejme/8446

Vancouver

Kapofu LK, Kapofu W. “This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study. INT ELECT J MATH ED. 2020;15(3):em0604. https://doi.org/10.29333/iejme/8446

AMA

Kapofu LK, Kapofu W. “This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study. INT ELECT J MATH ED. 2020;15(3), em0604. https://doi.org/10.29333/iejme/8446

Chicago

Kapofu, Lifeas Kudakwashe, and Winfilda Kapofu. "“This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0604. https://doi.org/10.29333/iejme/8446

Harvard

Kapofu, L. K., and Kapofu, W. (2020). “This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study. International Electronic Journal of Mathematics Education, 15(3), em0604. https://doi.org/10.29333/iejme/8446

MLA

Kapofu, Lifeas Kudakwashe et al. "“This Maths is better than that Maths” – Exploring Learner Perceptions on the Integration of History of Mathematics in Teaching the Theorem of Pythagoras: A Case Study". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0604. https://doi.org/10.29333/iejme/8446